TSTP Solution File: BOO007-4 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : BOO007-4 : TPTP v8.1.2. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 10:41:59 EDT 2024
% Result : Unsatisfiable 30.61s 4.75s
% Output : Refutation 30.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 9
% Syntax : Number of formulae : 72 ( 72 unt; 0 def)
% Number of atoms : 72 ( 71 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 168 ( 168 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f116625,plain,
$false,
inference(trivial_inequality_removal,[],[f116624]) ).
fof(f116624,plain,
multiply(a,multiply(b,c)) != multiply(a,multiply(b,c)),
inference(forward_demodulation,[],[f116060,f2]) ).
fof(f2,axiom,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_multiply) ).
fof(f116060,plain,
multiply(a,multiply(b,c)) != multiply(a,multiply(c,b)),
inference(superposition,[],[f9,f85893]) ).
fof(f85893,plain,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X2,X1)),
inference(backward_demodulation,[],[f79196,f85240]) ).
fof(f85240,plain,
! [X2,X0,X1] : multiply(X2,multiply(X0,X1)) = multiply(multiply(X2,X1),multiply(X0,X1)),
inference(superposition,[],[f85006,f206]) ).
fof(f206,plain,
! [X0,X1] : add(multiply(X1,X0),X0) = X0,
inference(superposition,[],[f163,f2]) ).
fof(f163,plain,
! [X0,X1] : add(multiply(X0,X1),X0) = X0,
inference(forward_demodulation,[],[f162,f6]) ).
fof(f6,axiom,
! [X0] : multiply(X0,multiplicative_identity) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_id1) ).
fof(f162,plain,
! [X0,X1] : multiply(X0,multiplicative_identity) = add(multiply(X0,X1),X0),
inference(forward_demodulation,[],[f137,f66]) ).
fof(f66,plain,
! [X0] : multiplicative_identity = add(X0,multiplicative_identity),
inference(forward_demodulation,[],[f56,f7]) ).
fof(f7,axiom,
! [X0] : multiplicative_identity = add(X0,inverse(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_inverse1) ).
fof(f56,plain,
! [X0] : add(X0,inverse(X0)) = add(X0,multiplicative_identity),
inference(superposition,[],[f48,f6]) ).
fof(f48,plain,
! [X0,X1] : add(X0,X1) = add(X0,multiply(inverse(X0),X1)),
inference(forward_demodulation,[],[f35,f22]) ).
fof(f22,plain,
! [X0] : multiply(multiplicative_identity,X0) = X0,
inference(superposition,[],[f2,f6]) ).
fof(f35,plain,
! [X0,X1] : add(X0,multiply(inverse(X0),X1)) = multiply(multiplicative_identity,add(X0,X1)),
inference(superposition,[],[f3,f7]) ).
fof(f3,axiom,
! [X2,X0,X1] : add(X0,multiply(X1,X2)) = multiply(add(X0,X1),add(X0,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity1) ).
fof(f137,plain,
! [X0,X1] : add(multiply(X0,X1),X0) = multiply(X0,add(X1,multiplicative_identity)),
inference(superposition,[],[f4,f6]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(X0,add(X1,X2)) = add(multiply(X0,X1),multiply(X0,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity2) ).
fof(f85006,plain,
! [X2,X0,X1] : multiply(X0,X1) = multiply(multiply(X0,add(X1,X2)),X1),
inference(forward_demodulation,[],[f83912,f156]) ).
fof(f156,plain,
! [X0,X1] : add(X0,multiply(X1,X0)) = X0,
inference(backward_demodulation,[],[f130,f155]) ).
fof(f155,plain,
! [X0,X1] : multiply(X0,add(X0,X1)) = X0,
inference(backward_demodulation,[],[f129,f154]) ).
fof(f154,plain,
! [X0,X1] : add(X0,multiply(X0,X1)) = X0,
inference(forward_demodulation,[],[f153,f6]) ).
fof(f153,plain,
! [X0,X1] : multiply(X0,multiplicative_identity) = add(X0,multiply(X0,X1)),
inference(forward_demodulation,[],[f131,f74]) ).
fof(f74,plain,
! [X0] : multiplicative_identity = add(multiplicative_identity,X0),
inference(superposition,[],[f66,f1]) ).
fof(f1,axiom,
! [X0,X1] : add(X0,X1) = add(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_add) ).
fof(f131,plain,
! [X0,X1] : add(X0,multiply(X0,X1)) = multiply(X0,add(multiplicative_identity,X1)),
inference(superposition,[],[f4,f6]) ).
fof(f129,plain,
! [X0,X1] : multiply(X0,add(X0,X1)) = add(X0,multiply(X0,X1)),
inference(superposition,[],[f3,f120]) ).
fof(f120,plain,
! [X0] : add(X0,X0) = X0,
inference(forward_demodulation,[],[f107,f5]) ).
fof(f5,axiom,
! [X0] : add(X0,additive_identity) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_id1) ).
fof(f107,plain,
! [X0] : add(X0,additive_identity) = add(X0,X0),
inference(superposition,[],[f50,f8]) ).
fof(f8,axiom,
! [X0] : additive_identity = multiply(X0,inverse(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_inverse1) ).
fof(f50,plain,
! [X0,X1] : add(X0,X1) = add(X0,multiply(X1,inverse(X0))),
inference(forward_demodulation,[],[f40,f6]) ).
fof(f40,plain,
! [X0,X1] : add(X0,multiply(X1,inverse(X0))) = multiply(add(X0,X1),multiplicative_identity),
inference(superposition,[],[f3,f7]) ).
fof(f130,plain,
! [X0,X1] : multiply(X0,add(X0,X1)) = add(X0,multiply(X1,X0)),
inference(forward_demodulation,[],[f128,f2]) ).
fof(f128,plain,
! [X0,X1] : multiply(add(X0,X1),X0) = add(X0,multiply(X1,X0)),
inference(superposition,[],[f3,f120]) ).
fof(f83912,plain,
! [X2,X0,X1] : multiply(multiply(X0,add(X1,X2)),X1) = multiply(X0,add(X1,multiply(multiply(X2,X0),X1))),
inference(superposition,[],[f78722,f206]) ).
fof(f78722,plain,
! [X2,X3,X0,X1] : multiply(multiply(X0,add(X1,X2)),add(multiply(X0,X1),X3)) = multiply(X0,add(X1,multiply(multiply(X2,X0),X3))),
inference(backward_demodulation,[],[f150,f78721]) ).
fof(f78721,plain,
! [X2,X3,X0,X1] : add(multiply(X0,X1),multiply(multiply(X0,X2),X3)) = multiply(X0,add(X1,multiply(multiply(X2,X0),X3))),
inference(backward_demodulation,[],[f31008,f78720]) ).
fof(f78720,plain,
! [X2,X3,X0,X1] : add(X1,multiply(multiply(X2,X0),X3)) = add(X1,multiply(multiply(X0,add(X1,X2)),X3)),
inference(forward_demodulation,[],[f78328,f3]) ).
fof(f78328,plain,
! [X2,X3,X0,X1] : add(X1,multiply(multiply(X0,add(X1,X2)),X3)) = multiply(add(X1,multiply(X2,X0)),add(X1,X3)),
inference(superposition,[],[f36,f3153]) ).
fof(f3153,plain,
! [X2,X0,X1] : add(X0,multiply(X1,X2)) = add(multiply(X2,add(X0,X1)),X0),
inference(forward_demodulation,[],[f3056,f41]) ).
fof(f41,plain,
! [X2,X0,X1] : add(X0,multiply(X2,X1)) = multiply(add(X0,X2),add(X1,X0)),
inference(superposition,[],[f3,f1]) ).
fof(f3056,plain,
! [X2,X0,X1] : multiply(add(X0,X1),add(X2,X0)) = add(multiply(X2,add(X0,X1)),X0),
inference(superposition,[],[f133,f193]) ).
fof(f193,plain,
! [X0,X1] : multiply(add(X0,X1),X0) = X0,
inference(forward_demodulation,[],[f192,f5]) ).
fof(f192,plain,
! [X0,X1] : add(X0,additive_identity) = multiply(add(X0,X1),X0),
inference(backward_demodulation,[],[f39,f185]) ).
fof(f185,plain,
! [X0] : additive_identity = multiply(X0,additive_identity),
inference(superposition,[],[f176,f2]) ).
fof(f176,plain,
! [X0] : additive_identity = multiply(additive_identity,X0),
inference(superposition,[],[f154,f10]) ).
fof(f10,plain,
! [X0] : add(additive_identity,X0) = X0,
inference(superposition,[],[f1,f5]) ).
fof(f39,plain,
! [X0,X1] : add(X0,multiply(X1,additive_identity)) = multiply(add(X0,X1),X0),
inference(superposition,[],[f3,f5]) ).
fof(f133,plain,
! [X2,X0,X1] : multiply(X0,add(X1,X2)) = add(multiply(X1,X0),multiply(X0,X2)),
inference(superposition,[],[f4,f2]) ).
fof(f36,plain,
! [X2,X0,X1] : add(X0,multiply(X1,X2)) = multiply(add(X1,X0),add(X0,X2)),
inference(superposition,[],[f3,f1]) ).
fof(f31008,plain,
! [X2,X3,X0,X1] : add(multiply(X0,X1),multiply(multiply(X0,X2),X3)) = multiply(X0,add(X1,multiply(multiply(X0,add(X1,X2)),X3))),
inference(forward_demodulation,[],[f31007,f1529]) ).
fof(f1529,plain,
! [X2,X3,X0,X1] : add(multiply(X0,X1),multiply(multiply(X0,X2),X3)) = multiply(multiply(X0,add(X1,X2)),add(X3,multiply(X0,X1))),
inference(superposition,[],[f41,f4]) ).
fof(f31007,plain,
! [X2,X3,X0,X1] : multiply(multiply(X0,add(X1,X2)),add(X3,multiply(X0,X1))) = multiply(X0,add(X1,multiply(multiply(X0,add(X1,X2)),X3))),
inference(forward_demodulation,[],[f31006,f5400]) ).
fof(f5400,plain,
! [X2,X0,X1] : multiply(X0,add(X1,X2)) = multiply(X0,add(X2,X1)),
inference(superposition,[],[f145,f4]) ).
fof(f145,plain,
! [X2,X0,X1] : multiply(X0,add(X1,X2)) = add(multiply(X0,X2),multiply(X0,X1)),
inference(superposition,[],[f4,f1]) ).
fof(f31006,plain,
! [X2,X3,X0,X1] : multiply(multiply(X0,add(X1,X2)),add(X3,multiply(X0,X1))) = multiply(X0,add(multiply(multiply(X0,add(X1,X2)),X3),X1)),
inference(forward_demodulation,[],[f30829,f2154]) ).
fof(f2154,plain,
! [X2,X3,X0,X1] : add(multiply(multiply(X0,X1),X2),multiply(X0,X3)) = multiply(X0,add(multiply(multiply(X0,X1),X2),X3)),
inference(superposition,[],[f36,f184]) ).
fof(f184,plain,
! [X2,X0,X1] : add(X0,multiply(multiply(X0,X1),X2)) = X0,
inference(forward_demodulation,[],[f179,f155]) ).
fof(f179,plain,
! [X2,X0,X1] : add(X0,multiply(multiply(X0,X1),X2)) = multiply(X0,add(X0,X2)),
inference(superposition,[],[f3,f154]) ).
fof(f30829,plain,
! [X2,X3,X0,X1] : multiply(multiply(X0,add(X1,X2)),add(X3,multiply(X0,X1))) = add(multiply(multiply(X0,add(X1,X2)),X3),multiply(X0,X1)),
inference(superposition,[],[f4,f235]) ).
fof(f235,plain,
! [X2,X0,X1] : multiply(X0,X1) = multiply(multiply(X0,add(X1,X2)),multiply(X0,X1)),
inference(superposition,[],[f193,f4]) ).
fof(f150,plain,
! [X2,X3,X0,X1] : add(multiply(X0,X1),multiply(multiply(X0,X2),X3)) = multiply(multiply(X0,add(X1,X2)),add(multiply(X0,X1),X3)),
inference(superposition,[],[f3,f4]) ).
fof(f79196,plain,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(multiply(X0,X1),multiply(X2,X1)),
inference(superposition,[],[f27604,f206]) ).
fof(f27604,plain,
! [X2,X0,X1] : multiply(X0,X1) = multiply(X0,multiply(X1,add(X0,X2))),
inference(forward_demodulation,[],[f27385,f154]) ).
fof(f27385,plain,
! [X2,X0,X1] : multiply(X0,multiply(X1,add(X0,X2))) = multiply(X0,add(X1,multiply(X1,X2))),
inference(superposition,[],[f223,f133]) ).
fof(f223,plain,
! [X2,X0,X1] : multiply(X0,add(X1,X2)) = multiply(X0,add(multiply(X0,X1),X2)),
inference(forward_demodulation,[],[f222,f139]) ).
fof(f139,plain,
! [X2,X0,X1] : multiply(X0,add(X2,X1)) = add(multiply(X0,X2),multiply(X1,X0)),
inference(superposition,[],[f4,f2]) ).
fof(f222,plain,
! [X2,X0,X1] : add(multiply(X0,X1),multiply(X2,X0)) = multiply(X0,add(multiply(X0,X1),X2)),
inference(forward_demodulation,[],[f217,f2]) ).
fof(f217,plain,
! [X2,X0,X1] : add(multiply(X0,X1),multiply(X2,X0)) = multiply(add(multiply(X0,X1),X2),X0),
inference(superposition,[],[f3,f163]) ).
fof(f9,axiom,
multiply(a,multiply(b,c)) != multiply(multiply(a,b),c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_associativity) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : BOO007-4 : TPTP v8.1.2. Released v1.1.0.
% 0.04/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n027.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Tue Apr 30 02:51:32 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.37 % (4394)Running in auto input_syntax mode. Trying TPTP
% 0.23/0.38 % (4397)WARNING: value z3 for option sas not known
% 0.23/0.38 % (4398)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.23/0.38 % (4401)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.23/0.38 % (4400)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.23/0.38 % (4399)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.23/0.38 % (4397)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.23/0.38 % (4395)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.23/0.38 % (4396)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.23/0.38 TRYING [1]
% 0.23/0.38 TRYING [2]
% 0.23/0.39 TRYING [3]
% 0.23/0.39 TRYING [1]
% 0.23/0.39 TRYING [2]
% 0.23/0.39 TRYING [3]
% 0.23/0.40 TRYING [4]
% 0.23/0.42 TRYING [4]
% 0.23/0.42 TRYING [5]
% 0.23/0.48 TRYING [6]
% 0.23/0.50 TRYING [5]
% 1.45/0.60 TRYING [7]
% 3.50/0.93 TRYING [6]
% 4.07/0.97 TRYING [8]
% 7.84/1.48 TRYING [1]
% 7.84/1.48 TRYING [2]
% 7.84/1.48 TRYING [3]
% 7.84/1.49 TRYING [4]
% 7.84/1.52 TRYING [5]
% 8.42/1.60 TRYING [6]
% 9.94/1.78 TRYING [9]
% 9.94/1.79 TRYING [7]
% 13.22/2.27 TRYING [8]
% 20.28/3.30 TRYING [9]
% 23.29/3.74 TRYING [7]
% 30.61/4.73 % (4400)First to succeed.
% 30.61/4.75 % (4400)Refutation found. Thanks to Tanya!
% 30.61/4.75 % SZS status Unsatisfiable for theBenchmark
% 30.61/4.75 % SZS output start Proof for theBenchmark
% See solution above
% 30.61/4.75 % (4400)------------------------------
% 30.61/4.75 % (4400)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 30.61/4.75 % (4400)Termination reason: Refutation
% 30.61/4.75
% 30.61/4.75 % (4400)Memory used [KB]: 37056
% 30.61/4.75 % (4400)Time elapsed: 4.359 s
% 30.61/4.75 % (4400)Instructions burned: 8474 (million)
% 30.61/4.75 % (4400)------------------------------
% 30.61/4.75 % (4400)------------------------------
% 30.61/4.75 % (4394)Success in time 4.366 s
%------------------------------------------------------------------------------